Parametrization of MIMO multi-controller schemes for bumpless switching

In this paper the realization and implementation of a multi-controller scheme made of a finite set of linear multiple-input-multiple-output controllers, possibly having different state dimensions, is considered. The problem of bumpless switching between the active controller acting in closed-loop and another controller in the set of controllers waiting to take over the control loop is addressed. A non minimal parametrization of the set of controllers such that all controllers share the same state variables is presented, and it is shown that such a parametrization guarantees bumpless switching between any two controllers within the controller set.